Using the paths below assume that the distance from Selma to Decatur is 40.9km. How far is it from Selma to Alexander city?

Find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1

kicyunya [14]

Given:

$f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1$

To find:

The correct function.

Explanation:

Let us consider the function given in option D.

$f(x)=\frac{x^2}{2}-4x+5$

Differentiating with respect to x we get,

$\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}$

Substituting x = 2 in the function f(x), we get

$\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}$

Therefore, the given conditions are satisfied.

So, the function is,

$f(x)=\frac{x^{2}}{2}-4x+5$

Final answer: Option D

6 0

2 years ago

find the curved surface area and total surface area of a right circular cylinder whose height is 15 cm and the radius of the bas

otez555 [7]

Answer:

$CSA = 660cm^2$ --- Curved Surface Area

$TSA = 968cm^2$ --- Total Surface Area

Step-by-step explanation:

Given

Shape: Cylinder

$h = 15$ -- height

$r = 7$ --- radius

Solving (a): The curved surface area (CSA)

This is calculated as:

$CSA = 2\pi rh$

This gives:

$CSA = 2 * \frac{22}{7} * 7 * 15$

$CSA = 2 * 22* 15$

$CSA = 660cm^2$

Solving (b): The total surface area (TSA)

This is calculated as:

$TSA = 2\pi r(h + r)$

This gives:

$TSA = 2 * \frac{22}{7} * 7 * (15 + 7)$

$TSA = 2 * 22 * (15 + 7)$

$TSA = 2 * 22 * 22$

$TSA = 968cm^2$

6 0

3 years ago

In circle K shown below, points B, C, D, and E lie on the circle with secants HBD and HCE drawn. Prove:

Alexxx [7]

Answer:

By exterior angle theorem, we have;

∠DBE = ∠H + ∠HEB = ∠ECD = ∠H + ∠HDC

∴ ∠H + ∠HEB = ∠H + ∠HDC

By addition property of equality, we have

∠HEB = ∠HDC

∠H = ∠H by reflexive property

∴ ΔHCD ~ ΔHEB by Angle Angle AA similarity postulate

∴ HE/HD = EB/DC, by the definition of similarity

Therefore, by cross multiplication, we have;

HE × DC = EB × HD

Therefore, by commutative property of multiplication, we have;

HE × DC = HD × EB

Step-by-step explanation:

3 0

3 years ago

There are 348 identical plastic chips numbered 1 through 348 in a box. What is the probability of reaching into the box and rand

hoa [83]

<h2>P(E) = $\dfrac{53}{87}$ or, 0.6092</h2>

Step-by-step explanation:

Given,

There are 348 identical plastic chips numbered 1 through 348 in a box.

To find, the probability of reaching into the box and randomly drawing a chip number which is smaller than 213 = ?

Total number of possible outcomes = 348

Let E be the event of getting randomly drawing a chip number that is smaller than 213.

Favourable outcomes are:

1, 2, 3, .............., 212

Number of favourable outcomes = 212

∴ Probability =

P(E) =

= $\dfrac{53}{87}$ or, 0.6092

Thus, P(E) = $\dfrac{53}{87}$ or, 0.6092

4 0

4 years ago

A square ceiling has a diagonal of 24 ft. Shelton wants to put molding around the perimeter of the ceiling.

Gala2k [10]

Answer:

16.97 feet

Step-by-step explanation:

a^2=b^2+c^2

24^2=576

b and c are equal divide 576 by 2 to get 288 square root of 288=16.97 feet

5 0

3 years ago